Physics

Gravitation and Orbital Mechanics

500 Questions

Gravitation and orbital mechanics focus on planetary motion, elliptical orbits, and satellite deployment. Questions examine astrodynamics fundamentals, including geostationary orbits and perturbation theory. These topics are highly relevant for civil services and specialized technical examinations.

Planetary orbitsSatellite dynamicsGeostationary orbitsPerturbation theoryOrbital eccentricity

Gravitation and Orbital Mechanics Questions

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Which one of the following statements is correct?

  1. The energy required to rocket an orbiting satellite out of earth's gravitational influence is more than the energy required to project a stationary object at the same height (as the satellite) out of earth's influence.

  2. If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of potential energy.

  3. The first artificial satellite Sputnik I was launched in the year 1950.
  4. The orbital speed of the SYNCOMS (synchronous communications satellite) is $3.07\times10^{2}m s^{-1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The energy required to rocket an orbiting satellite out of earth's gravitational influence is less than the energy required to project a stationary object at the same height (as the satellite) out of earth's influence.
Hence, option (a) is incorrect statement.


If zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic energy.
Hence, option (b) is an incorrect statement.

The first artificial satellite was launched by Soviet scientists in the year 1957.
Hence, option (c) is an incorrect statement.

The orbital speed of the SYNCOMS is $v=\dfrac{2\pi{r}}{T}=\dfrac{2\times3.14\times4.22\times10^{7}}{8.64\times10^{5}}$
$=3.07\times10^{2}m s^{-1}$
Hence, option (d) is a correct statement.

Multiple choice evs search of life outside earth types of artificial satellites geostationary orbits moon and stars in sky

Out of the following, the only correct statement about satellites is

  1. A satellite cannot move in a stable orbit in a plane passing through the earth's centre

  2. Geostationary satellites are launched in the equatorial plane

  3. Satellites are rectangular in shape.

  4. Geostationary satellites are launched in axial plane
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Geostationary satellites are launched to the equitorial plane, so the it could have a time period of 24 hours exact and can have maximum reach, i.e on both heminpheres for information transfer.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The time period of an orbiting satellite is (assuming spherical earth)

  1. Directly proportional to the density of earth

  2. Directly proportional to the square of density of earth

  3. Inversely proportional to the square root of density of earth

  4. Inversely proportional to the density of earth
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The time period of a satellite orbiting close to a spherical body is proportional to the square root of the inverse of density. Specifically, T equals 2 times pi times the square root of (R cubed over G M), which can be rewritten using density as T being inversely proportional to the square root of the density of the earth. Therefore, option C is correct while the other proportionality relations are incorrect.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A satellite is orbiting around the earth in an orbit in equatorial plane, of radius 2$R _{e}$ , where $R _{e}$ is theradius of the earth. Find the area on the earth, this satellite covers for communication purpose in its complete revolution 

  1. $4\pi R _{e}^{2}$
  2. $2\pi\sqrt{3} R _{e}^{2}$
  3. $2\pi(2-\sqrt{3}) R _{e}^{2}$
  4. $2\pi(4+\sqrt{3}) R _{e}^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Two satellites A & B go around the earth in a circular orbits at a heigh of $R _{A} & R _{B}$ respectively from surface of the earth. Assume earth to be a uniform sphere of radius $R _{e}$ The ratio of the magnitudes of velocities of the satellite $V _{A}/V _{B}$ is

  1. $\sqrt{\frac{R _{A}}{R _{B}}}$
  2. $\left ( R _{A}/R _{B} \right )^{2}$
  3. $\frac{R _{B}+R _{e}}{R _{A}+R _{e}}$
  4. $\sqrt{\frac{R _{B}+R _{e}}{R _{A}+R _{e}}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The orbital velocity of a satellite at distance r from the center of the earth is given by the square root of (G M over r). Here, the distances from the earth's center are r_A = R_A + R_e and r_B = R_B + R_e. Taking the ratio V_A over V_B gives the square root of (r_B over r_A), which matches option D.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

To have an earth synchronous satellites it should be launched at the proper height moving from

  1. North to South in a polar plane

  2. East to West in an equatorial plane

  3. South to North in a polar plane

  4. West to East in an equatorial plane
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sense of synchronous satellite must be same as the sense of rotation of earth i.e., from west to east

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The time period of geostationary satellite is :

  1. Zero
  2. $24 h$
  3. $12 h$
  4. $48 h$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Answer is B.

A geostationary orbit can only be achieved at an altitude very close to $35,786$ km $(22,236 mi)$, and directly above the Equator. This equates to an orbital velocity of $3.07 km/s (1.91 mi/s)$ or an orbital period of $1,436$ minutes, which equates to almost exactly one sidereal day or $23.934461223$ hours, which is approximately $24$ hours.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The period of rotation of the geostationary satellite is ______ hours.

  1. 12

  2. 24

  3. 6

  4. 48
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A geostationary satellite is an earth-orbiting satellite, placed at an altitude of approximately 35,800 kilometers (22,300 miles) directly over the equator, that revolves in the same direction the earth rotates (west to east). 

At this altitude, one orbit takes $24 hours $, the same length of time as the earth requires to rotate once on its axis. 
The term geostationary comes from the fact that such a satellite appears nearly stationary in the sky as seen by a ground-based observer. 

Hence correct answer is option $B$ 

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The orbital angular velocity vector of a geostationary satellite and the spin angular velocity vector of the earth are

  1. always in the same direction

  2. always in opposite direction

  3. always mutually perpendicular

  4. inclined at 23 1/2 to each other
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the satellite to be 'synchronous' with the Earth, its period of revolution should be equal to Earth's rotation. For this, the satellite has to revolve along the direction of Earth's rotation thus their angular velocity vector always point in the same direction.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A synchronous satellite should be at a proper height moving

  1. From West to East in equatorial plane

  2. From South to North in polar plane

  3. From East to West in equatorial plane

  4. From North to South in polar plane
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the satellite to be 'synchronous' with the Earth, its period of revolution should be equal to Earth's rotation. For this, the satellite has to revolve along the direction of Earth's rotation that is from West to East.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A satellite placed in an orbit around Earth with certain speed will revolve in_______ as seen from Earth

  1. A helical path

  2. A circular path

  3. Straight line

  4. A parabolic path
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The centrifugal force acting on the satellite, revolving around the earth with certain velocity, is balanced by the gravitational force acting on it due to earth. The satellite keeps revolving around the earth in circular path of certain radius as seen from the earth.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Parking orbit for a geostationary satellite is

  1. at 45 degrees north west of equator

  2. is in equatorial plane of earth

  3. in west-east direction.

  4. along the north direction
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Parking orbit for a geostationary satellite is in equatorial plane of earth, since it has to be at rest always with respect to equator

The correct option is option (b)